Melt electrospinning writing (MEW) using an automated stage has recently been developed as a direct additive manufacturing method for the fabrication of orderly, precise and complex porous 3D fibrous structures that can promote cell infiltration and growth. The further incorporation of inorganic particles within fibrous scaffolds is desirable in order to enhance bioactivity, however this remains challenging with the MEW fabrication process. To address this challenge, flexible, osteoconductive, medical grade polycaprolactone (m-PCL) - hydroxyapatite (HAp) composite 3D fibrous structures with high porosity (96–98%) and fully interconnected pore architectures were fabricated using MEW under precisely controlled parameters. The physical properties of these 3D fibrous composite scaffolds including fibre size, mechanical characteristics, and in vitro degradation rate were investigated. The results showed that the composite m-PCL/HAp fibrous scaffolds degraded in an alkaline environment at 37 °C faster than plain m-PCL and provided a favourable platform for the infiltration and growth of human osteoblasts. Moreover, confocal imaging confirmed that the scaffolds contained HAp nano-particles (NPs) which induced a more homogeneous distribution of cells within the scaffold particularly after 7 days of culture. Osteoblast activity and viability in the m-PCL/HAp composite scaffolds indicated a favourable cell/material interaction, suggesting great potential for use in mineralised tissue reconstruction / regeneration applications.